Question

1. Consider a three firm (n = 3) Cournot oligopoly. The market inverse demand function is

p (Q) = 24 Q.

Firm 1 has constant average and marginal costs of $12 per unit, while firms 2 and 3 have constant average and marginal costs of $15 per unit.

a)Verify that the following are Nash equilibrium quantities for this market: q1 = 9 / 2 and q2 = q3 = 3 / 2 .

b)How much profit does each firm earn in equilibrium?

(c) Suppose firms 2 and 3 merge. We now have a duopoly in which firm 1 has costs of $12 per unit and firm 2 (the merged entity) has costs of $15 per unit.

i. Nash equilibrium quantities for each firm in this duopoly: q1 = 9 and q2= 6, and calculate each firm's equilibrium profit. Was the merger a good idea for the two merging firms? Be sure to explain your answer.

ii. Calculate the consumer surplus for the pre-merger market (i.e., the one with 3 firms) and for the post-merger market (i.e., the one with 2 firms).

[Hint: In each case, you need to draw the market demand curve, identify the market price based on the equilibrium quantities, and then calculate the area of the consumer surplus triangle.]

ii. Suppose the Commerce Commission allows a merger to take place if it increases total surplus, where total surplus is the sum of industry profit plus consumer surplus. (" Industry profits " is the total profit of all firms in the industry - the sum of the individual firms' profits.) It will not allow the merger if total surplus falls or stays the same. Will the Commerce Commission approve the merger in this case? Be sure to explain your answer.

Answer 1

Cournot oli opoy Page No. ums nにP-PC) q_ (24-12-91-92-93) 94 2-9-43)- Bimi lasty OD Bolwing 6A Bimultaneouolys then - 9-9-94 go 3-13-89 39-3-9, 80 4-3 6-9 6- a9

= 16-5 a- 3 (6 5-15) (312) 2.25

Page No. Now then P 848 thenBB (C) 13-9m1-1 en BRo (.) NOUDees rosd idea, Boz eft Por Menped Bad

24 cs (Post Mersge Cs 84 구 구-5

So CS( pre merger) = .5*(24-16.5)*7.5 = 28.125

CS (post merger)= .5*(24-17)*7= 24.5

Thus CS falls post merger

Page No. (premo geo_-est industry T = (89. 185) t (a3 :25) +2 ( 2.95): 58.845 ニ 84-5ナ85t4 = 53.5